"Guma de șters a creionului este mică."
Translation:The eraser on the pencil is small.
I have an idea since I ask myself the same: Maybe it is because the article "Gum-a-" is followed by another part of the construction "de șters". So the genitive can not follow directly after the article. But to show the connection they probably include the possesion "a" in this special case "Guma de șters a creionului"
When I went to school in England and Australia (some sixty five years ago) we used to call the eraser a rubber. You only heard the term eraser in American films. I suppose that the term has disappeared from use because of some other connotations. It was a perfectly good term, because it actually provided two descriptions in one word: the action of rubbing out and the material which was some sort of rubber.
This response is more or less copied from another DL thread:
The possessive marker "al, a, ai, ale" is used when the possessed noun has a definite article AND the possessed noun is placed right before the possessor. Both of these conditions must be satisfied to avoid use of the possessive marker "al, a, ai, ale."
In other words, if EITHER of these two conditions are not met, then the possessive marker "al, a, ai, ale" must be used.
Examples: cartea copilului (lit. "the book of the child"), not cartea a copilului. If either condition is not met, then the possessive article appears: o carte a copilului (lit. "a book of the child") (the possessed noun does not have a definite article); cartea frumoasă a copilului (lit. "the beautiful book of the child") (the possessed noun is not placed right before the possessor); o carte frumoasă a copilului (lit. "a beautiful book of the child") (the possessed noun does not have a definite article and is not placed right before the possessor).
Another helpful way to think about: Always use the possessive marker "al, a, ai, ale" to show possession unless the possessor is both directly adjacent to the noun possessed AND the noun that is possessed is definite.
In some ways, this is analogous to English. When showing possession of an indefinite noun in English, you cannot say, "a my friend." No, you must instead say, "a friend of mine" (un prieten al meu).